Verified quantum random number generation for cryptographic applications

Abstract

Systems and methods for quantum random number generation are provided. In some implementations, a method can include obtaining data indicative of a quantum circuit used by the quantum random number generation system to generate a quantum entropy source for determining a random number. The quantum entropy source can include a plurality of output samples. Each output sample can be obtained by measuring an output of the quantum circuit. The method can include performing one or more simulations of the quantum circuit to obtain a simulated output distribution of the quantum circuit without access to data associated with the random number. The method can include providing data indicative of the simulated output distribution for use in a verification process for the quantum random number generation system. The verification process can determine the use of the quantum computing system in generation of the quantum entropy source.

What is claimed is: 
     
       1. A method for determining use of a quantum computing system in a quantum random number generation system, the quantum random number generation system being implemented at least in part using the quantum computing system having one or more qubits, the method comprising:
 obtaining, by one or more computing devices comprising one or more classical processors, data indicative of a quantum circuit used by the quantum random number generation system to perform a quantum operation to generate a quantum entropy source for determining a private random number, the quantum circuit comprising one or more quantum gates, the quantum entropy source comprising a plurality of output samples, each output sample obtained by measuring an output of the quantum circuit; 
 performing, by the one or more computing devices, one or more simulations of the quantum circuit to obtain a simulated output distribution of the quantum circuit without access to data associated with the private random number; and 
 providing, by the one or more computing devices, data indicative of the simulated output distribution for use in a verification process for the quantum random number generation system, the verification process determining the use of the quantum computing system in generation of the quantum entropy source; 
 wherein the one or more computing devices are associated with a verification computing system that is distinct from a computing system associated with a user of the quantum random number generation system, wherein the data associated with the private random number is maintained confidential and is not shared with the one or more computing devices associated with the verification computing system; and 
 wherein the data associated with the private random number comprises the private random number or a seeded randomness extractor used to generate the private random number. 
 
     
     
       2. The method of  claim 1 , wherein the verification process comprises performing a benchmarking test based at least in part the simulated output distribution and the quantum entropy source. 
     
     
       3. The method of  claim 2 , wherein the benchmarking test comprises a cross-entropy benchmarking test. 
     
     
       4. The method of  claim 1 , wherein the verification process is implemented based on only a subset of the plurality of output samples of the simulated output distribution. 
     
     
       5. The method of  claim 1 , wherein the one or more simulations are performed using a Schrodinger-Feynman algorithm. 
     
     
       6. The method of  claim 1 , wherein the one or more simulations are performed using a Feynman algorithm. 
     
     
       7. The method of  claim 1 , wherein providing, by the one or more computing devices, data indicative of the simulated output distribution comprises providing a plurality of simulated output samples for use in the verification process. 
     
     
       8. The method of  claim 1 , wherein the verification process comprises:
 determining a set of probabilities for the plurality of output samples; 
 performing a benchmarking test on the set of probabilities. 
 
     
     
       9. The method of  claim 7 , wherein providing, by the one or more computing devices, data indicative of the simulated output distribution comprises providing data associated with a hash tree structure generated based on the simulated output distribution, the hash tree structure comprising:
 a plurality of leaf nodes, each leaf node associated with a cryptographic hash of a simulated output sample; and 
 a plurality of intermediate nodes, each intermediate node associated with an aggregate result based on at least one child node of the intermediate node. 
 
     
     
       10. A computing system for generating a private random number from a quantum entropy source, the quantum entropy source generated at least in part using a quantum computing system having one or more qubits, the computing system comprising:
 one or more processors; and 
 one or more memory devices, the one or more memory devices storing computer-readable instructions that when executed by the one or more processors cause the one or more processors to perform operations, the operations comprising:
 providing data indicative of a quantum circuit used to perform a quantum operation in the quantum computing system to generate the quantum entropy source, the quantum circuit comprising one or more quantum gates; 
 obtaining the quantum entropy source from the quantum computing system, the quantum entropy source comprising a plurality of output samples of the quantum computing system after implementation of the quantum circuit; 
 providing data indicative of the quantum circuit used to perform the quantum operation to generate the quantum entropy source to a verification computing system without providing access to data associated with the private random number, the verification computing system being distinct from the computing system for generating a private random number; 
 obtaining data associated with one or more simulations of the quantum circuit from the verification computing system; and 
 performing a verification process for the private random number based at least in part on the data associated with the one or more simulations, the verification process determining the use of the quantum computing system in generation of the quantum entropy source. 
 
 
     
     
       11. The computing system of  claim 10 , determining the private random number based at least in part on the quantum entropy source. 
     
     
       12. The computing system of  claim 11 , wherein the quantum entropy source is not shared with the verification computing system. 
     
     
       13. A method for generating a quantum entropy source for random number generation using a quantum computing system, the quantum computing system comprising one or more qubits, the method comprising:
 obtaining, by one or more computing devices, data indicative of an entropy requirement for the quantum entropy source; 
 determining, by the one or more computing devices, a number of output samples to be measured of the one or more qubits after implementing a quantum circuit in the quantum computing system based at least in part on the data indicative of the entropy requirement, the quantum circuit comprising one or more quantum gates; 
 obtaining, by the one or more computing devices, a plurality of measurements of the one or more qubits after implementing the quantum circuit based on the number of output samples; and 
 providing, by the one or more computing devices, the plurality of measurements as output samples for the quantum entropy source to be used in random number generation; 
 wherein the entropy requirement comprises a min-entropy requirement; and 
 wherein the number of output samples is determined based on the min-entropy requirement, a fidelity associated with the quantum circuits, and a number of qubits in the quantum computing system. 
 
     
     
       14. The method of  claim 13 , wherein the number of output samples is determined based on the min-entropy requirement and a fidelity associated with the quantum circuit. 
     
     
       15. The method of  claim 13 , wherein the quantum entropy source comprises a plurality of bit strings.